ELEN 661  Modulation Theory
Homework #7
Assignment Date: 3/26/08
Due Date: 4/2/08
1.
(a) Sketch the phase trellis diagrams for CPFSK with modulation indices of
,
and
.
(b) Calculate the asymptotic power efficiency,
, for each of the three modula
tion indices given in part (a).
2. Consider a full response CPM signalling format where the phase pulse shape is given by
.
(a) Compute the asymptotic power efficiency of this signalling format assuming a modulation
index of
. That is calculate
. How does the asymptotic performance
compare with MSK?
(b) Using MATLAB generate a realization of the CPM signal described above (again take
) and use that realization to plot the PSD of the CPM signal. Based on your result com
pute the bandwidth at which the PSD is at least 30dB down from its peak value anywhere outside
the band. Compare that result with the bandwidth (30dB down) for an MSK signal.
3. Consider a GMSK signalling scheme which uses
. Sketch a block diagram of the
optimum coherent receiver for this signalling format. Be sure to specify how many correlators are
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 Spring '08
 Miller
 Probability, Probability theory, Heaviside step function, asymptotic power efficiency

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